Inference procedure has parameters:
Ice fuel: 200
Timeout: 60s
Convolution: right


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)])}
(plus([_mda, _nda, _oda]) /\ plus([_mda, _nda, _pda])) -> eq_nat([_oda, _pda])
)
(le, P:
{() -> le([z, s(nn2)])
(le([nn1, nn2])) -> le([s(nn1), s(nn2)])
(le([s(nn1), s(nn2)])) -> le([nn1, nn2])
(le([s(nn1), z])) -> BOT
(le([z, z])) -> BOT}
)
}

properties:
{(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda])}


over-approximation: {plus}
under-approximation: {}

Clause system for inference is:

{
() -> le([z, s(nn2)]) -> 0
() -> plus([n, z, n]) -> 0
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 0
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 0
(le([s(nn1), z])) -> BOT -> 0
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 0
(le([z, z])) -> BOT -> 0
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 0
}


Solving took 0.347716 seconds.
Proved
Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5823, q_gen_5824, q_gen_5833, q_gen_5834, q_gen_5839},
Q_f={q_gen_5820, q_gen_5823},
Delta=
{
<s>(q_gen_5833) -> q_gen_5833
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, s>(q_gen_5839) -> q_gen_5839
<z, s>(q_gen_5833) -> q_gen_5839
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<s, s, s>(q_gen_5823) -> q_gen_5823
<s, z, s>(q_gen_5839) -> q_gen_5823
<z, s, s>(q_gen_5824) -> q_gen_5823
<z, s, s>(q_gen_5839) -> q_gen_5823
<z, z, s>(q_gen_5833) -> q_gen_5823
<s, s, s>(q_gen_5820) -> q_gen_5834
<s, s, s>(q_gen_5834) -> q_gen_5834
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005666 s (model generation: 0.005275,  model checking: 0.000391):

Model:
|_
{
le -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 0
() -> plus([n, z, n]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 1
(le([z, z])) -> BOT -> 1
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.011161 s (model generation: 0.011033,  model checking: 0.000128):

Model:
|_
{
le -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820},
Q_f={q_gen_5820},
Delta=
{
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 1
(le([z, z])) -> BOT -> 1
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.011372 s (model generation: 0.011138,  model checking: 0.000234):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822},
Q_f={q_gen_5821},
Delta=
{
<z>() -> q_gen_5822
<z, s>(q_gen_5822) -> q_gen_5821
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820},
Q_f={q_gen_5820},
Delta=
{
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 1
(le([z, z])) -> BOT -> 1
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]), {
_lda -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.011790 s (model generation: 0.011475,  model checking: 0.000315):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822},
Q_f={q_gen_5821},
Delta=
{
<z>() -> q_gen_5822
<z, s>(q_gen_5822) -> q_gen_5821
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824},
Q_f={q_gen_5820},
Delta=
{
<z, z>() -> q_gen_5824
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 2
(le([z, z])) -> BOT -> 2
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 4, which took 0.014588 s (model generation: 0.011198,  model checking: 0.003390):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822},
Q_f={q_gen_5821},
Delta=
{
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824},
Q_f={q_gen_5820},
Delta=
{
<z, z>() -> q_gen_5824
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 3
(le([s(nn1), z])) -> BOT -> 3
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 3
(le([z, z])) -> BOT -> 3
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 5, which took 0.012215 s (model generation: 0.011714,  model checking: 0.000501):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822},
Q_f={q_gen_5821},
Delta=
{
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824},
Q_f={q_gen_5820},
Delta=
{
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 4
(le([z, z])) -> BOT -> 4
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 4
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 6, which took 0.012431 s (model generation: 0.012094,  model checking: 0.000337):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824},
Q_f={q_gen_5820},
Delta=
{
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 4
(le([z, z])) -> BOT -> 4
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]), {
_lda -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 7, which took 0.014572 s (model generation: 0.012823,  model checking: 0.001749):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824, q_gen_5833},
Q_f={q_gen_5820},
Delta=
{
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, s, s>(q_gen_5820) -> q_gen_5820
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, s>(q_gen_5833) -> q_gen_5820
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 7
(le([z, z])) -> BOT -> 5
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 7
}
Sat witness: Found: ((le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]), {
_qda -> s(z)  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 8, which took 0.013912 s (model generation: 0.013632,  model checking: 0.000280):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<z, z>() -> q_gen_5821
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824, q_gen_5833},
Q_f={q_gen_5820},
Delta=
{
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, s, s>(q_gen_5820) -> q_gen_5820
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, s>(q_gen_5833) -> q_gen_5820
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 5
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 5
(le([s(nn1), z])) -> BOT -> 5
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 7
(le([z, z])) -> BOT -> 8
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 7
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

-------------------------------------------
Step 9, which took 0.013809 s (model generation: 0.013640,  model checking: 0.000169):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5836},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<s, s>(q_gen_5836) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<z, z>() -> q_gen_5836
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824, q_gen_5833},
Q_f={q_gen_5820},
Delta=
{
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, s, s>(q_gen_5820) -> q_gen_5820
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, s>(q_gen_5833) -> q_gen_5820
<z, z, z>() -> q_gen_5820
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 5
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 8
(le([s(nn1), z])) -> BOT -> 6
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 7
(le([z, z])) -> BOT -> 8
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 7
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 10, which took 0.015871 s (model generation: 0.013443,  model checking: 0.002428):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824, q_gen_5832, q_gen_5833},
Q_f={q_gen_5820},
Delta=
{
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, s, s>(q_gen_5832) -> q_gen_5820
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<s, s, s>(q_gen_5820) -> q_gen_5832
<z, z, s>(q_gen_5833) -> q_gen_5832
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 7
() -> plus([n, z, n]) -> 7
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 8
(le([s(nn1), z])) -> BOT -> 7
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 7
(le([z, z])) -> BOT -> 8
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 10
}
Sat witness: Found: ((plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]), {
_lda -> s(s(z))  ;  mm -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 11, which took 0.015470 s (model generation: 0.015018,  model checking: 0.000452):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5823, q_gen_5824, q_gen_5833, q_gen_5834},
Q_f={q_gen_5820, q_gen_5823},
Delta=
{
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, s>(q_gen_5833) -> q_gen_5824
<z, z>() -> q_gen_5824
<z, z, z>() -> q_gen_5820
<s, s, s>(q_gen_5823) -> q_gen_5823
<s, z, s>(q_gen_5824) -> q_gen_5823
<z, s, s>(q_gen_5824) -> q_gen_5823
<z, z, s>(q_gen_5833) -> q_gen_5823
<s, s, s>(q_gen_5820) -> q_gen_5834
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 7
() -> plus([n, z, n]) -> 7
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 8
(le([s(nn1), z])) -> BOT -> 7
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 10
(le([z, z])) -> BOT -> 8
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 10
}
Sat witness: Found: ((le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]), {
_qda -> s(s(z))  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 12, which took 0.017731 s (model generation: 0.016653,  model checking: 0.001078):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5823, q_gen_5824, q_gen_5833, q_gen_5834},
Q_f={q_gen_5820, q_gen_5823},
Delta=
{
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, s>(q_gen_5833) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, s, s>(q_gen_5823) -> q_gen_5820
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<z, s, s>(q_gen_5824) -> q_gen_5823
<z, z, s>(q_gen_5833) -> q_gen_5823
<s, s, s>(q_gen_5820) -> q_gen_5834
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> plus([n, z, n]) -> 8
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 8
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 9
(le([s(nn1), z])) -> BOT -> 8
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 10
(le([z, z])) -> BOT -> 9
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 13
}
Sat witness: Found: ((plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]), {
_lda -> s(s(z))  ;  mm -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 13, which took 0.020422 s (model generation: 0.019389,  model checking: 0.001033):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5824, q_gen_5832, q_gen_5833, q_gen_5839},
Q_f={q_gen_5820},
Delta=
{
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<z, s>(q_gen_5833) -> q_gen_5839
<s, s, s>(q_gen_5832) -> q_gen_5820
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, s, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<s, s, s>(q_gen_5820) -> q_gen_5832
<s, z, s>(q_gen_5839) -> q_gen_5832
<z, s, s>(q_gen_5839) -> q_gen_5832
<z, z, s>(q_gen_5833) -> q_gen_5832
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 9
() -> plus([n, z, n]) -> 9
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 9
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 9
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 13
(le([z, z])) -> BOT -> 10
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 13
}
Sat witness: Found: ((le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]), {
_qda -> s(s(z))  ;  m -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 14, which took 0.023074 s (model generation: 0.022303,  model checking: 0.000771):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835, q_gen_5836},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5836) -> q_gen_5835
<z, z>() -> q_gen_5836
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5823, q_gen_5824, q_gen_5833, q_gen_5834},
Q_f={q_gen_5820, q_gen_5823},
Delta=
{
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, s>(q_gen_5833) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, s, s>(q_gen_5834) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<s, s, s>(q_gen_5823) -> q_gen_5823
<s, z, s>(q_gen_5824) -> q_gen_5823
<z, s, s>(q_gen_5824) -> q_gen_5823
<z, z, s>(q_gen_5833) -> q_gen_5823
<s, s, s>(q_gen_5820) -> q_gen_5834
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 10
() -> plus([n, z, n]) -> 10
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 10
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 10
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 13
(le([z, z])) -> BOT -> 11
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 13
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> s(z)
})

-------------------------------------------
Step 15, which took 0.021367 s (model generation: 0.020288,  model checking: 0.001079):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5823, q_gen_5824, q_gen_5827, q_gen_5833, q_gen_5834},
Q_f={q_gen_5820, q_gen_5823},
Delta=
{
<z>() -> q_gen_5833
<z, z>() -> q_gen_5824
<s, s>(q_gen_5824) -> q_gen_5827
<z, s>(q_gen_5833) -> q_gen_5827
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<s, s, s>(q_gen_5823) -> q_gen_5823
<s, z, s>(q_gen_5827) -> q_gen_5823
<z, s, s>(q_gen_5824) -> q_gen_5823
<z, s, s>(q_gen_5827) -> q_gen_5823
<z, z, s>(q_gen_5833) -> q_gen_5823
<s, s, s>(q_gen_5820) -> q_gen_5834
<s, s, s>(q_gen_5834) -> q_gen_5834
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 10
() -> plus([n, z, n]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 11
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 11
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 13
(le([z, z])) -> BOT -> 11
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 13
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(s(z)))
})

-------------------------------------------
Step 16, which took 0.022880 s (model generation: 0.021882,  model checking: 0.000998):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5823, q_gen_5824, q_gen_5827, q_gen_5833, q_gen_5834},
Q_f={q_gen_5820, q_gen_5823},
Delta=
{
<z>() -> q_gen_5833
<z, z>() -> q_gen_5824
<s, s>(q_gen_5824) -> q_gen_5827
<s, s>(q_gen_5827) -> q_gen_5827
<z, s>(q_gen_5833) -> q_gen_5827
<s, s, s>(q_gen_5823) -> q_gen_5820
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<s, z, s>(q_gen_5827) -> q_gen_5823
<z, s, s>(q_gen_5824) -> q_gen_5823
<z, s, s>(q_gen_5827) -> q_gen_5823
<z, z, s>(q_gen_5833) -> q_gen_5823
<s, s, s>(q_gen_5820) -> q_gen_5834
<s, s, s>(q_gen_5834) -> q_gen_5834
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 11
() -> plus([n, z, n]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 12
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 12
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 13
(le([z, z])) -> BOT -> 12
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 16
}
Sat witness: Found: ((plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]), {
_lda -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 17, which took 0.026336 s (model generation: 0.025643,  model checking: 0.000693):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5823, q_gen_5824, q_gen_5827, q_gen_5833, q_gen_5834},
Q_f={q_gen_5820, q_gen_5823},
Delta=
{
<s>(q_gen_5833) -> q_gen_5833
<z>() -> q_gen_5833
<s, s>(q_gen_5827) -> q_gen_5824
<z, z>() -> q_gen_5824
<s, s>(q_gen_5824) -> q_gen_5827
<z, s>(q_gen_5833) -> q_gen_5827
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<s, s, s>(q_gen_5823) -> q_gen_5823
<s, z, s>(q_gen_5827) -> q_gen_5823
<z, s, s>(q_gen_5824) -> q_gen_5823
<z, s, s>(q_gen_5827) -> q_gen_5823
<z, z, s>(q_gen_5833) -> q_gen_5823
<s, s, s>(q_gen_5820) -> q_gen_5834
<s, s, s>(q_gen_5834) -> q_gen_5834
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 12
() -> plus([n, z, n]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 13
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 13
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 16
(le([z, z])) -> BOT -> 13
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 16
}
Sat witness: Found: ((le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]), {
_qda -> s(s(s(z)))  ;  m -> s(z)  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 18, which took 0.030325 s (model generation: 0.028945,  model checking: 0.001380):

Model:
|_
{
le -> 
{{{
Q={q_gen_5821, q_gen_5822, q_gen_5835},
Q_f={q_gen_5821},
Delta=
{
<s>(q_gen_5822) -> q_gen_5822
<z>() -> q_gen_5822
<s, s>(q_gen_5821) -> q_gen_5821
<z, s>(q_gen_5822) -> q_gen_5821
<s, s>(q_gen_5835) -> q_gen_5835
<z, z>() -> q_gen_5835
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5820, q_gen_5823, q_gen_5824, q_gen_5833, q_gen_5834, q_gen_5839},
Q_f={q_gen_5820, q_gen_5823},
Delta=
{
<s>(q_gen_5833) -> q_gen_5833
<z>() -> q_gen_5833
<s, s>(q_gen_5824) -> q_gen_5824
<z, z>() -> q_gen_5824
<z, s>(q_gen_5833) -> q_gen_5839
<s, z, s>(q_gen_5824) -> q_gen_5820
<z, z, z>() -> q_gen_5820
<s, s, s>(q_gen_5823) -> q_gen_5823
<s, z, s>(q_gen_5839) -> q_gen_5823
<z, s, s>(q_gen_5824) -> q_gen_5823
<z, s, s>(q_gen_5839) -> q_gen_5823
<z, z, s>(q_gen_5833) -> q_gen_5823
<s, s, s>(q_gen_5820) -> q_gen_5834
<s, s, s>(q_gen_5834) -> q_gen_5834
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 13
() -> plus([n, z, n]) -> 14
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 14
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 14
(le([s(nn1), z])) -> BOT -> 14
(le([z, m]) /\ le([z, n]) /\ plus([n, m, _qda])) -> le([n, _qda]) -> 16
(le([z, z])) -> BOT -> 14
(plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]) -> 19
}
Sat witness: Found: ((plus([n, mm, _lda])) -> plus([n, s(mm), s(_lda)]), {
_lda -> s(s(z))  ;  mm -> s(z)  ;  n -> z
})

Total time: 0.347716
Reason for stopping: Proved